Principal Component Analysis of Event-by-Event Fluctuations

We apply principal component analysis to the study of event-by-event fluctuations in relativistic heavy-ion collisions. This method brings out all the information contained in two-particle correlations in a physically transparent way. We present a guide to the method, and apply it to multiplicity fluctuations and anisotropic flow, using ALICE data and simulated events. In particular, we study elliptic and triangular flow fluctuations as a function of transverse momentum and rapidity. This method reveals previously unknown subleading modes in both rapidity and transverse momentum for the momentum distribution as well as elliptic and triangular flows.

Figure 1

Principal component analysis as a function of pseudorapidity for $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ in the 0%–10% centrality window generated with AMPT. (a) Multiplicity fluctuations. (b) Elliptic flow fluctuations. (c) Triangular flow fluctuations.

Figure 2

Principal component analysis as a function of transverse momentum for $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ in the 0%–10% centrality window, using ALICE data [13] (full symbols) and AMPT events (open symbols). (a) Multiplicity fluctuations. (b) Elliptic flow fluctuations. (c) Triangular flow fluctuations.